System and method performing Quadrature Amplitude Modulation by combining co-sets and strongly coded co-set identifiers

ABSTRACT

A method of encoding a stream of data elements is provided which involves splitting the stream of data elements into a first stream and a second stream; encoding the first stream to produce a first encoded stream; performing a constellation mapping using a combination of the first encoded stream and a third stream which is based on the second stream. This may involve defining a signal constellation; defining a plurality of co-sets within the constellation such that a minimum distance between constellation points within each co-set is larger than a minimum distance between any constellation points within the signal constellation; performing said constellation mapping by using the first encoded stream to identify a sequence of co-sets of said plurality of co-sets, and by using the third stream to identify a sequence of constellation points within respective co-sets of the sequence of co-sets identified by said first encoded stream.

RELATED APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 12/856,982 filed on Aug. 16, 2010, now U.S. Pat.No. 8,290,078, which is a continuation of Ser. No. 10/226,174 filed onAug. 23, 2002, now U.S. Pat. No. 7,778,341, which claims the benefit ofprior U.S. Provisional Application Nos. 60/314,169 and 60/314,168 filedon Aug. 23, 2001, all of which are incorporated in their entirety as iffully and completely set forth herein.

FIELD OF THE INVENTION

The invention relates to systems and methods for combining binary errorcorrecting codes (such as turbo codes) and multi-level signal sets, suchas QAM (Quadrature Amplitude Modulation), PSK (Phase Shift Keying), PAM(Pulse Amplitude Modulation).

BACKGROUND OF THE INVENTION

Conventional systems and methods for the combination of binary errorcorrecting codes (such as turbo codes) and multi-level signal sets (suchas QAM) typically operate as depicted in FIG. 1. Input data is encoded,for example using Turbo Encoding. The encoded output is interleaved andmapped m bits at a time to a QAM constellation using a QAM constellationmapping which is typically a Gray mapping. The result is transmittedover a channel. At the receiver, the QAM de-mapping is performed,followed by turbo decoding.

In these schemes, Turbo decoding is achieved in two stages. First, theprobability values corresponding to the bits are extracted by adding upthe probability of the corresponding constellation points. Then, thesebit probability values are passed to a conventional Turbo-decoder foriterative decoding. The complexity of these methods grows with the sizeof the constellation due to the step required in extracting theprobability values. In addition, the extra interleaving stage requiredbetween the binary encoder and the constellation (to reduce thedependency between the adjacent bits mapped to the same constellation)adds to the overall system complexity. It is well known that the codinggain of these schemes drops as the spectral efficiency increases.

Disadvantageously, noise in the QAM may result in multiple bit errorswhich may not be correctable. For example, in a constellation with 1024points, capable of representing ten bits per symbol, an error in themapping may result in up to all ten bits being in error. Most currentsystems map similar bit sequences to constellation points which areclose to each other to mitigate this problem somewhat. Gray Mapping isan example of this.

Notwithstanding Gray mapping, the error rates achieved with such systemsare still significantly less than the limit said to be theoreticallyachievable by Shannon's coding theorem. As QAM size increases, thecoding loss becomes significant.

SUMMARY OF THE INVENTION

One broad aspect of the invention provides a method of encoding a streamof data elements. The method involves splitting the stream of dataelements into a first stream and a second stream; encoding the firststream to produce a first encoded stream; performing a constellationmapping using a combination of the first encoded stream and a thirdstream which is based on the second stream.

In some embodiments, the constellation mapping performs a Gray mappingin mapping the third stream.

In some embodiments, the third stream is identical to the second stream.

In some embodiments, the method further involves encoding the secondstream to produce the third stream using relatively weak encodingcompared to that used in encoding the first stream to produce the thirdstream.

In some embodiments, the method further involves performing shaping onthe second stream to produce the third stream.

In some embodiments, the method further involves performing shaping andchannel coding on the second stream to produce the third stream withrelatively weak encoding compared to that used in encoding the firststream.

In some embodiments, the encoding performed on the first stream is turboencoding.

In some embodiments, the shaping is performed using a Huffman tree basedaddressing scheme to get a substantially Gaussian amplitudedistribution.

In some embodiments, performing constellation shaping for a given signalconstellation comprising a plurality of constellation points involvesassociating a cost with each of the plurality of constellation points;defining a hierarchy of blocks, the hierarchy having a plurality oflayers comprising at least a first layer and a last layer, each layerhaving fewer blocks than each previous layer; wherein the first layer isformed by ordering all of the constellation points according to cost,and then assigning a first lowest cost group of constellation points toa first shaping partition, a second lowest cost group of constellationpoints to a second shaping partition dividing comprises a plurality ofshaping partitions, and so on until a highest cost group ofconstellation points assigned to a last shaping partition, each shapingpartition being assigned a cost based on the costs of the constellationpoints in the shaping partition, each shaping partition being a firstlayer block; wherein an element in each other layer is formed bycombining two blocks of a previous layer and is assigned a cost based onthe costs of the two blocks of the previous layer, a block of each layerbeing comprised of one of the elements according to cost, or a group ofthe elements according to cost; the last layer having a single blockcomprising a plurality of elements; shaping gain being achieved by onlymapping to a subset of the elements of the last layer.

In some embodiments, the constellation mapping uses the data elements ofthe first encoded stream for least significant bits of the constellationmapping and the constellation mapping uses the data elements of thethird stream for most significant bits of the constellation mapping.

In some embodiments, the method further involves defining a signalconstellation comprising a plurality of constellation points; defining aplurality of co-sets within the plurality of constellation points suchthat a minimum distance between constellation points within each co-setis larger than a minimum distance between any constellation pointswithin the signal constellation; performing said constellation mappingby using the first encoded stream to identify a sequence of co-sets ofsaid plurality of co-sets, and by using the third stream to identify asequence of constellation points within respective co-sets of thesequence of co-sets identified by said first encoded stream.

In some embodiments, labels of constellation points within each co-setare Gray mapped.

In some embodiments, the constellation mapping uses the data elements ofthe first encoded stream for least significant bits of the constellationmapping and the constellation mapping uses the data elements of thethird stream for most significant bits of the constellation mapping.

In some embodiments, the plurality of constellation points comprises aregular array, and wherein each co-set comprises a respective set ofequally spaced points within the regular array.

In some embodiments, the Turbo encoding is symbol-based Turbo encoding.

Another broad aspect of the invention provides a transmitter which has ade-multiplexer adapted to split an input stream into a first stream anda second stream; a first encoder adapted to encode the first stream toproduce a first encoded stream; a constellation mapper adapted toperform constellation mapping using a combination of the first encodedstream and a third stream which is based on the second stream.

Another broad aspect of the invention provides a receiver which has afirst constellation de-mapper adapted to perform de-mapping of areceived signal to extract a first sub-stream; a decoder adapted toperform decoding of the first sub-stream to produced a decodedsub-stream; a re-encoder adapted to re-encode the decoded sub-stream toproduce a sequence of co-set identifiers; a second constellationde-mapper adapted to perform constellation de-mapping of the receivedsignal within co-sets of constellation points identified by the sequenceof co-set to extract a second sub-stream.

Another broad aspect of the invention provides a transmitter havingmeans for splitting a stream of data elements into a first stream and asecond stream; means for encoding the first stream to produce a firstencoded stream; and means for performing a constellation mapping using acombination of the first encoded stream and a third stream which isbased on the second stream.

Any of the above summarized or below described embodiments can beimplemented on an appropriate computer readable medium, for example amemory storage medium such as a disk. They can also be implemented inany appropriate processing platform such as a general purpose processor,custom processor or FPGA, DSP, ASIC to name a few examples.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the invention will be described with referenceto the attached drawings in which:

FIG. 1 is a block diagram of a conventional QAM coding scheme;

FIG. 2A is a block diagram of a constellation coding scheme provided bya first embodiment of the invention;

FIG. 2B is an example of how a simple QAM constellation may be used forthe embodiment of FIG. 2A;

FIGS. 2C, 2D, 2E and 2F provide example performance results for theembodiment of FIG. 2A;

FIG. 3 is a block diagram of a constellation coding scheme provided by asecond embodiment of the invention;

FIG. 4 is a block diagram of a constellation coding scheme provided by athird embodiment of the invention; and

FIG. 5 is a simple example of how encoding is performed for theembodiment of FIG. 4.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to FIG. 2A, a first embodiment of the invention is shownin block diagram form. Shown is transmitter/encoder functionalitygenerally indicated by 80, a channel generally indicated by 98 which forthe purpose of this example may be assumed to be a band-limited AWGNchannel, and receiver/decoder functionality generally indicated by 82.

The transmitter/encoder takes an input stream 84 and splits it with bitdemultiplexer 85 into first and second parallel streams 86,88 L₁ and K₁bits wide respectively. The second stream 88 is turbo encoded with turboencoder 90 to produce a K₂-bit stream 91 or more generally is encoded bysome type of encoding which is stronger than any error correction codingused for the first stream 86 which in the illustrated example has noencoding. The underlying Turbo-code is preferably a symbol-based Turbocode which preferably interleaves the bits grouped in symbols used toselect the co-sets (symbol size of two bits is preferred). Aconstellation selector 96 (also referred to as a constellation mapper)implements a signal constellation by mapping sets of input bits torespective constellation points within the signal constellation. Theconstellation signal set mapped to by the constellation selector 96 ispartitioned into co-sets to be selected by the group of bits (symbols)of the symbol-based Turbo-code. For example, the Turbo-code mayinterleave bits in pairs, and the constellation may be a PAM signal setpartitioned into 4 co-sets to be selected by the 2 bits of thesymbol-based Turbo-code. The properties of an example two bit by twosymbol-based interleaving are presented in U.S. Pat. No. 6,298,463entitled “Symbol-based Turbo-codes” to Bingeman et al. assigned to thesame assignee as this application, and hereby incorporated by referencein its entirety. For the second parallel bit stream, K_(1/)R=K₂, where Ris the coding rate of the turbo code. The two streams 86,91 aremultiplexed together in bit multiplexer 97 the output of which is inputto a constellation selector 96 which operates as described by way ofexample below with reference to FIG. 2B. The constellation selector 96may implement any suitable constellation, for example QAM, PAM, PSK orothers. Alternatively, two separate inputs to the constellation selector96 may be employed.

The constellation selector 96 maps to a set of 2^(L) ² ×2^(K) ² possibleconstellation points. A physical interpretation of splitting up the bitstream in the above manner is that the available constellation pointsare divided up into 2^(K) ² different co-sets each containing 2^(L) ²constellation points. A simple example of such co-sets is shown in FIG.2B for QAM modulation. In this example, L₂=2 and K₂=2, so we have a 16QAM constellation 40 which is divided up into 2^(K) ² =4 co-sets 42, 44,46, 48 containing 2^(L) ² =4 constellation points each. In this case,the input to the mapping is four bits {l⁰, l¹, k⁰, k¹} of which l⁰, l¹are the most significant bits which originate from the uncoded stream,and of which k⁰, k¹ are the least significant bits which originate fromthe coded stream. The least significant bits, indicated at 49 are usedto select one of the four co-sets 42,44,46,48. The most significantbits, indicated at 51 are used to select a point within the co-setidentified by the least significant bits. This is illustrated for thecase where the co-set 42 is selected by the least significant bits. Moregenerally, the constellation selector 96 mapping uses the data elementsof the Turbo encoded stream for a given subset of the bits (for examplethe least significant bits) of the constellation point labels and theconstellation selector 96 uses the data elements of the remaining streamfor the rest of the bits (for example the most significant bits) of theconstellation point labels.

The data elements of the Turbo encoded stream 91 are used as a stream ofco-set identifiers. The data elements of the first stream 86 are used toidentify points within the sequence of co-sets. Preferably, a Graymapping is employed in mapping the first stream 86 to a given co-set.This involves ensuring the mapping maps bit patterns which differ byonly one bit to adjacent symbols within a co-set. This amounts to alabeling convention, there is no Gray coding step or Gray de-codingstep, these being inherently taken care of by the selection of labelsfor the constellation points.

It is noted that in FIG. 2A and subsequent figures, the variousfunctional blocks are shown separately. More generally, these blocks maybe implemented in any set of one or more physical blocks, and may beimplemented for example a general purpose processor, a DSP, ASIC, FPGAor other processing platform.

Advantageously, the minimum distance of the constellation points withina given co-set can be significantly larger than the minimum distance ofthe constellation points within the constellation as a whole.

In FIG. 2A, at the receiver/decoder 82, first, a constellationde-mapping is performed in constellation de-mapper 108 of only the K₂Turbo coded bits. Turbo decoding is performed by turbo decoder 102 toturbo decode the K₁ least significant bits to produce a K₁ bit decodedstream. The probability values required to initialize the Turbo decodermay for example be computed by adding the probability of constellationpoints within each co-set and then the conventional iterative decodingprocedure follows. This is then re-encoded with turbo encoder 104 whichis identical to the turbo encoder 90 at the input. This produces a K₂bit wide sequence which is output as the sequence of co-set identifiers.These are used to select a co-set with co-set selector 107 therebyidentifying a set of points which are used as the constellation for themost significant bits. Then, based on the co-set thus selected, the L₂most significant bits are de-mapped with constellation soft de-mapping111. Hard decisions are made in decision block 110 and the L₂=L₁ bitoutput is fed to a bit multiplexer 112. The K₁ bit output of the turbodecoder 102 is also fed to the bit multiplexer 112 the output of whichis the recovered bit stream.

Some example performance results are shown in FIG. 2C where a 16 PAMconstellation was used. The capacity for the least significant bit group(the turbo-encoded group) is plotted in curve 72, and the capacity forthe most significant bit group is plotted in curve 70. The capacity forthe combined channel is plotted in curve 74, and the theoretical Shannonlimit for the AWGN is shown in curve 76. Similar results are shown inFIG. 2D for 4 PAM. Bit error rate performance is shown in FIGS. 2E and2F for two examples. FIG. 2E applies for the BER of Turbo coded QAM forrate 4/6 64 QAM (spectral efficiency of 4 bits/sec/Hz) with interleaversize N=2000 (bits). FIG. 2F applies for the BER of Turbo coded QAM forrate 12/14 16384 QAM (spectral efficiency of 12 bits/sec/Hz) withinterleaver size N=2000 (bits).

Referring now to FIG. 3, a second embodiment of the invention is shownin block diagram form. This embodiment has many blocks in common withthe embodiment of FIG. 2A, and such blocks are identically numbered.This embodiment features a channel encoder 89 in the transmitter/encoder80 between the bit demultiplexer 85 and the bit multiplexer 97. Thechannel encoder 89 may, for example, perform block coding on the L₁ bitstream output by the bit multiplexer 85 to produce the L₂ bit channelcoded stream which is then input to the bit multiplexer 97. In thiscase, unlike in the first embodiment where L₂=L₁, L₂=L₁/R₂ where R₂ isthe rate of the code implemented in the channel encoder 89.

As before, the second parallel stream 88 is turbo encoded with turboencoder 90, or more generally is encoded by some type of encoding whichis stronger than that used in the channel encoder 89. Where blockencoding has been used in the illustrated example, more generally, anyencoding which is weaker than that used for the second parallel bitstream 88 may be employed. Then, similar to the previous embodiment, thechannel encoded bit stream 86 is used to select constellation pointswithin a sequence of co-sets identified by the turbo encoded bit stream.

At the receiver/decoder 82, the processing of the turbo coded bit streamis the same as in the first embodiment described above. For the channelencoded stream, however, the constellation soft/de-mapping function 108in this case may be soft and/or hard de-mapping function 111. This isfollowed by a channel decoder which decodes at rate R₂ to produce the L₂bit stream input to the bit multiplexer 112.

Another embodiment of the invention will now be described with referenceto FIG. 4. Again, this embodiment shares many blocks in common with theembodiment of FIG. 2A, and these blocks are identically numbered. On thetransmitter/encoder side 80, there is optionally a channel encoder 89performing channel coding as described above with rate R₂, and there isa constellation shaping block 113 which performs constellation shapingby mapping shaping bits into a sequence of shaping partitions. The orderof the blocks 89,113 may be reversed, but the preferred order is shown.The output of the constellation shaping block 113 is an L₁′ bit stream,and the output of the channel encoder 89 is an L₂ bit stream 93 which isinput to the bit multiplexer 97 as before, together with the sequence ofco-set identifiers generated by the turbo encoder 90. The processing forthe second stream output by the bit demultiplexer 85 is the same as forthe first two embodiments.

The inclusion of the constellation shaping block 113 changes the natureof the co-sets somewhat. Where in previous embodiments, the differentco-sets were static entities, in this embodiment, the different co-setsare shaped by the constellation shaping block 113. In other words, theL₂ bits (in FIG. 4) select the sequence of shaping partitions and thenthe turbo coded bits select the co-sets within each shaping partition.This is guaranteed to be possible as long as each shaping partitioncontain and equal number of points from each co-set. A detailed exampleis presented below with reference to FIG. 5. Various shaping techniquesmay be employed. Commonly assigned U.S. Pat. No. 7,151,804 filed thesame day as this application discloses a method of shaping which may beemployed. That application is hereby incorporated by reference in itsentirety.

The application teaches a method of performing constellation shaping fora signal constellation comprising a plurality of constellation points.The method involves associating a cost with each of the plurality ofconstellation points; defining a hierarchy of blocks, the hierarchyhaving a plurality of layers comprising at least a first layer and alast layer, each layer having fewer blocks than each previous layer;wherein the first layer is formed by ordering all of the constellationpoints according to cost, and then assigning a first lowest cost groupof constellation points to a first shaping partition, a second lowestcost group of constellation points to a second shaping partitiondividing comprises a plurality of shaping partitions, and so on until ahighest cost group of constellation points assigned to a last shapingpartition, each shaping partition being assigned a cost based on thecosts of the constellation points in the shaping partition, each shapingpartition being a first layer block; wherein an element in each otherlayer is formed by combining two blocks of a previous layer and isassigned a cost based on the costs of the two blocks of the previouslayer, a block of each layer being comprised of one of the elementsaccording to cost, or a group of the elements according to cost; thelast layer having a single block comprising a plurality of elements;shaping gain being achieved by only mapping to a subset of the elementsof the last layer.

In some embodiments the cost assigned to each constellation point is itsenergy.

In some embodiments, at least some of the layers blocks are simplyreordered combined blocks of a previous layer.

In some embodiments, for layers in which blocks are groups of re-orderedcombined blocks of a previous layer, all groups are the same size.

In some embodiments, in at least one layer in which blocks are groups ofre-ordered combined blocks of a previous layer, the groups havedifferent sizes.

The method may further involve performing addressing by applying a firstsubset of a set of input bits to identify an element in the block of thehighest layer; applying subsequent subsets of the set of input bits toidentify blocks in subsequent layers, with a particular shapingpartition being identified in the first layer; at the first layer,applying a final subset of input bits to identify a particular signalconstellation point within the particular shaping partition identifiedin the first layer.

In some embodiments, Huffman tree based addressing is employed. In otherembodiments, fixed tree based addressing is employed.

In some embodiments, a 256 point constellation is employed, there are 16layer one partitions each comprising 16 constellation points, there are8 layer two blocks each containing 16 elements, there are 4 layer 3blocks each containing 8 elements, the 8 elements having sizes{16,16,32,32,32,32,32,64}, there are 2 layer 4 blocks each containing 64elements, and there is one layer 5 block containing 4096 elements.

In some embodiments, the input bits comprise a plurality of data bitsand at least one dummy bit, and the method further involves repeatingthe method of b 16 for each permutation of values of the at least onedummy bit.

In some embodiments, the method is repeated for each of a plurality ofsignal constellations to generate a respective plurality of shapedoutputs for each signal constellation. Peak average power reduction isthen performed by appropriate selection of a single shaped output fromeach respective plurality of shaped outputs.

At the receiver 82 of FIG. 4, the decoding of the turbo encoded bitsproceeds as in previous examples to produce a sequence of co-sets whichis input to a constellation soft de-mapping of the remaining L₂ bits.The soft values output by the soft de-mapping step are input to achannel decoder which decodes the rate R₂ code. This outputs an L₁′ bitchannel decoded stream which is then input to an inverse addressingblock 110 which performs the opposite operation of the constellationshaping block 113 to produce the L₁ bit stream which is input to the bitmultiplexer 112 together with the K₁ bit turbo decoded stream.

FIG. 5 shows a very simple example of how mapping may be employed usingthe structure of FIG. 4. In this embodiment, we have a 16 PAMconstellation, and the 16 PAM constellation points are shown lined up,generally indicated at 500. A 16 PAM constellation point can representfour bits. Constellation points are selected by the combination of a twobit coding label 502, and a two bit shaping label 504.

There are four shaping labels 00, 01, 10, 11. The first shaping label 00is applied to the four PAM constellation points with lowest energy,namely those in the center of the PAM constellation. The second shapinglabel 01 is applied to the four PAM constellation points with the nextlowest energy, these being the two on either side of the first four. Thethird shaping label 10 is applied to the four PAM constellation pointswith the next lowest energy, these being the two on either side of thesecond four. Finally, the last shaping label 11 is applied to the fourPAM constellation points with the highest.

There are also only four coding labels in this example, i.e. only fourco-set identifiers, and these are labeled 00,01,10,11. These are appliedto the PAM symbols such that for each shaping label, there is exactlyone symbol have each coding label/co-set identifier. More generally,there should be an equal number of points from each co-set within eachshaping partition. Under this condition, it can be seen that shaping andcoding work independently where the co-set identifier operates on theconstellation points within the shaping partition selected by theshaping block. In the event there is more than one coding label in thesame shaping partition, then extra bits employed to select between themultiple points. For example, the same labeling scheme of FIG. 5 can beemployed for a 32 PAM constellation, but an extra bit from the input isthen used to select between two PAM constellation points for eachshaping label, coding label combination. In this case, the shaping labelis used to select a particular shaping partition and then the codinglabel (output by turbo encoder) is used to select a co-set within thatshaping partition, and in the event there is still ambiguity, the extrabits (which may also be considered part of the shaping label) are usedto select the final point.

FIGS. 2A, 3 and 4 include various functionalities at the receiver forrecovering the transmitted information. It is to be understood that manydifferent receiver structures may be used to recover the informationencoded using the encoding techniques shown in FIGS. 2A, 3 and 4.

In one embodiment, where shaping followed by channel encoding wasemployed at the transmitter, the probability values are computed for allthe bits (systematic as well as parities) of the Turbo coded bits. Theresulting probabilities are then mixed with the conditional probabilityof points within the co-sets using Bayes formula. Then, theprobabilities of points are properly added to compute the probabilitiesof bits for the channel stream. The resulting probabilities are thenpassed to a soft decision decoder for the channel code acting within theco-sets. Finally, the resulting decoded bits are passed to an inverseshaping block to recover the shaping bits.

In one embodiment, where shaping followed by channel encoding wasemployed at the transmitter, the probability values are computed for allthe bits (systematic as well as parities) of the Turbo codes bits. Theresulting probabilities are then mixed with the conditional probabilityof points within the co-sets using Bayes formula. Then, theprobabilities of points are properly added to compute the probabilitiesof bits for the channel coded stream. The resulting probabilities arethen passed to a soft output decoder for the channel code acting withinthe co-sets. Finally, the resulting bit probabilities are passed to aninverse shaping block which in this case is a finite state system usedto perform maximum likelihood decoding of the shaping bits. This finitestate system is the same as the finite state system used to perform theaddressing.

In one embodiment, where shaping followed by channel encoding wasemployed at the transmitter, the probability values are computed for allthe bits (systematic as well as parities) of the Turbo coded bits. Theresulting probabilities are then mixed with the conditional probabilityof points within the co-set using Bayes formula. Then, the probabilitiesof points are properly added to compute the probabilities of bits forthe channel coded stream. The resulting probabilities are then passed toa soft output decoder for the channel code acting within the co-sets.Finally, the resulting bit probabilities are passed to an inverseshaping block which in this case is a finite state system used toperform soft output decoding of the shaping bits. This finite statesystem is the same as the finite state system used to perform theaddressing. It is also possible to have an iterative decoding betweendifferent soft output decoders.

Numerous modifications and variations of the present invention arepossible in light of the above teachings. It is therefore to beunderstood that within the scope of the appended claims, the inventionmay be practised otherwise than as specifically described herein.

We claim:
 1. A method of decoding a stream of data elements comprising:receiving a first signal; performing constellation de-mapping for afirst subset of the first signal; decoding the first subset of the firstsignal to produce a decoded first subset of the first signal;determining a set of points for constellation de-mapping for a secondsubset of the first signal based on the decoded first subset of thefirst signal; performing constellation de-mapping for the second subsetof the first signal using the set of points; recovering a bit streamfrom the first signal based on said performing constellation de-mappingfor the first subset of the first signal and based on said performingconstellation de-mapping for the second subset of the first signal. 2.The method of claim 1, wherein said decoding the first subset of thefirst signal comprises performing turbo decoding of the first subset ofthe first signal.
 3. The method of claim 1, wherein said determining theset of points for constellation de-mapping comprises performing turboencoding of the decoded first subset of the first signal.
 4. The methodof claim 1, wherein the first subset of the first signal comprises theleast significant bits of the first signal.
 5. The method of claim 1,wherein the second subset of the first signal comprises the mostsignificant bits of the first signal.
 6. The method of claim 1, whereinsaid receiving the first signal is performed over a band-limited AWGNchannel.
 7. A receiver, comprising: reception circuitry configured toreceive a first signal; a first constellation de-mapper, configured toperform constellation de-mapping for a first subset of the first signal;a decoder, configured to decode the first subset of the first signal toproduce a decoded first subset of the first signal; a first element,configured to determine a set of points for constellation de-mapping fora second subset of the first signal based on the decoded first subset ofthe first signal; a second constellation de-mapper, configured toperform constellation de-mapping for the second subset of the firstsignal using the set of points; a second element, configured to recovera bit stream from the first signal based on said performingconstellation de-mapping for the first subset of the first signal andbased on said performing constellation de-mapping for the second subsetof the first signal.
 8. The receiver of claim 7, wherein said decodingthe first subset of the first signal comprises performing turbo decodingof the first subset of the first signal.
 9. The receiver of claim 7,wherein said determining the set of points for constellation de-mappingcomprises performing turbo encoding of the decoded first subset of thefirst signal.
 10. The receiver of claim 7, wherein the first subset ofthe first signal comprises the least significant bits of the firstsignal.
 11. The receiver of claim 7, wherein the second subset of thefirst signal comprises the most significant bits of the first signal.12. The receiver of claim 7, wherein the first element comprises anencoder and a co-set selector, wherein the encoder is configured toencode the decoded first subset of the first signal to produce anencoded decoded first subset of the first signal, wherein the co-setselector is configured to determine the set of points for constellationde-mapping for the second subset of the first signal using the encodeddecoded first subset of the first signal.
 13. The receiver of claim 7,wherein the second element comprises a decision element to determinebits from the second subset of the first signal and a bit multiplexerconfigured to receive the output of the decision element and the decoderto recover the bit stream from the first signal.
 14. A non-transitory,computer accessible memory medium storing program instructions fordecoding a stream of data elements, wherein the program instructions areexecutable to: receive a first signal; perform constellation de-mappingfor a first subset of the first signal; decode the first subset of thefirst signal to produce a decoded first subset of the first signal;determine a set of points for constellation de-mapping for a secondsubset of the first signal based on the decoded first subset of thefirst signal; perform constellation de-mapping for the second subset ofthe first signal using the set of points; recover a bit stream from thefirst signal based on said performing constellation de-mapping for thefirst subset of the first signal and based on said performingconstellation de-mapping for the second subset of the first signal. 15.The non-transitory, computer accessible memory medium of claim 14,wherein said decoding the first subset of the first signal comprisesperforming turbo decoding of the first subset of the first signal. 16.The non-transitory, computer accessible memory medium of claim 14,wherein said determining the set of points for constellation de-mappingcomprises performing turbo encoding of the decoded first subset of thefirst signal.
 17. The non-transitory, computer accessible memory mediumof claim 14, wherein the first subset of the first signal comprises theleast significant bits of the first signal.
 18. The non-transitory,computer accessible memory medium of claim 14, wherein the second subsetof the first signal comprises the most significant bits of the firstsignal.
 19. The non-transitory, computer accessible memory medium ofclaim 14, wherein said receiving the first signal is performed over aband-limited AWGN channel.